Rewrite the following without an exponent.5^-2

Answer:

No entiendo ingles perdon

Answer:

D. 8

Step-by-step explanation:

Using the graph of the function above, f(4) can be easily determined by tracing the corresponding coordinate of x = 4. When x = 4, on the x-axis, y = 8 on the y-axis.

The value of f(4), simply means, what is the value of y when x = 4.

Thus, the value of f(4) = 8.

The right answer is D. 8.

Answer: A. Vertical angles

Step-by-step explanation:

They are vertically opposite angles.

Correct me if I am incorrect.

Answer: So you're looking for 43/19 but not to the nearest hundredth, so maybe your teacher is looking for the decimal to be rounded to the nearest tenth or one thousandth... Here's how you would solve this...

Step-by-step explanation:

49/13 or 49 ÷ 13

49/13 = 3.76923076923

To the Nearest 10th: Answer ≈ 3.8

To the Nearest 1,000th: Answer ≈ 3.769

To the Nearest 100th: Answer ≈ 3.77

Note: I listed the nearest 100th in case you need it, I hope this helps you!

Thus, the magnitude of vector with the given x-Component = -6 units and  y-component = -8 units​ is found as: 10 units.

The length of a vector determines its magnitude. The letter "a" stands for the vector's magnitude.

We shall take the square root of sum of the squares of each component of a two-dimensional vector to estimate its magnitude from its coordinates. For instance, the following formula can be used to determine a vector's magnitude: U = (x1, y1).

|U| = √[x1² + y1²]

The Pythagorean theorem serves as the basis for this formula.

given vectors:

magnitude = √[x² + y²]

magnitude = √[(-6)² + (-8)²]

magnitude = √[36 + 64]

magnitude = √100

magnitude = 10 units

Thus, the magnitude of vector with the given x-Component = -6 units and  y-component = -8 units​ is found as: 10 units.

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Complete question:

find the magnitude of vector?

x-Component = -6 units, y-component = -8 units​

Answer:

Rational

Explanation: because it can be expressed in the quotient of two integers:67÷1

Answer:

The right answer is the first option, 14,32.

Step-by-step explanation:

FH is a hypotenuse.

\(FG^2+GH^2=FH^2\\ FG^2 = FH^2-GH^2\\ FG^2 = 23^2-18^2\\ FG^2= 529-324\\ FG^2=205\\ FG=\sqrt{205}\)

\(\sqrt{205} = 14,317...=14,32\)

The number the spinner is most likely to land on is 2

From the question, we have the following parameters that can be used in our computation:

The spinner

From the spinner, we have the number that covers the largest area to be 2

i.e.

Largest area = 2

This means that the number it is most likely to land on is 2 and it has the highest probability

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a) An equation relating the miles traveled to gallons of gas used is m = 14g.

b) With 3.7 gallons of gas, one can drive up to 51.8 miles.

An equation is a mathematical statement that makes two mathematical expressions equivalent or equal using the equation symbol (=).

Equations establish the equality of two or more values, variables, or numbers.

The total distance driven on one tank of gas = 168 miles

The quantity of gas used = 12 gallons

The number of miles per gallon of gas = 14 (168/12)

Let m = distance in miles

Let g = gallons of gas used

Equation: m = 14g

Solution:

Gallons of gas used = 3.7

m = 14g

= 14(3.7)

= 51.8 miles

Thus, based on the established equation, with 3.7 gallons of gas used, the driver can cover 51.8 miles.

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The value of lim F(t) for F(t) if F is a solution to the logistic differential equation dF/dt is 10 in option (c).

Finding through differential equation

\(\small \text{Consider the differential equation}\\ \frac{\mathrm{d} F}{\mathrm{d} t}=0.2\left ( 5F-\frac{F^2}{2} \right ),\quad F(0)=47\\ \frac{\mathrm{d} F}{\mathrm{d} t}=\frac{0.2}{2}\left ( 10F-F^2 \right )\\ \frac{\mathrm{d} F}{\mathrm{d} t}=\frac{F}{10}\left ( 10-F \right )\\\)

\(\text{Separable the variables of F and t on both sides}\\ \int \frac{1}{F(10-F)}\: dF=\frac{1}{10}\int \: dt\\ \frac{1}{10}\int \frac{10}{F(10-F)}\: dF=\frac{1}{10}\int \: dt\\ \frac{1}{10}\int \frac{(10-F)+F}{F(10-F)}\: dF=\frac{1}{10}\int \: dt\\ \int \frac{1}{10F}dF-\int \frac{1}{10\left(F-10\right)}dF=\frac{1}{10}\int \: dt\\ \int \frac{1}{F}dF-\int \frac{1}{\left(F-10\right)}dF= \int \: dt\\\)

\(\small \ln \left|F\right|- \ln \left|F-10\right|=t+\ln C\\ \ln \left|\frac{F}{F-10}\right| =\ln \left |Ce^{t} \right |\\ \frac{F}{F-10}=Ce^{t}\\ F(0)=47\Rightarrow \frac{47}{47-10}=C\Rightarrow C=\frac{47}{37}\\ \text{Therefore,}\\ \frac{F}{F-10}=\frac{47}{37}e^{t}\\ F=\frac{47}{37}e^{t}(F-10)\\ F=\frac{47}{37}e^{t} F-\frac{470}{37}e^{t}\\ F\left ( \frac{47}{37}e^{t}-1 \right ) =\frac{470}{37}e^{t}\\ =\frac{\frac{470}{37}e^{t}}{\left ( \frac{47}{37}e^{t}-1 \right )}\\\)

\(\small F(t) =\frac{\frac{470}{37}}{\left ( \frac{47}{37}-e^{-t} \right )}\\ \lim_{t\rightarrow \infty }F(t)=\lim_{t\rightarrow \infty } \frac{\frac{470}{37}}{\left ( \frac{47}{37}-e^{-t} \right )}\\ = \frac{\frac{470}{37}}{\left ( \frac{47}{37}-0 \right )}\\ = \frac{\frac{470}{37}}{\frac{47}{37}}\\ =\frac{470}{47}\\ =10\\\)

If F is a solution to the logistic differential equation then dF/dt is 10 in option (c).

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Mrs. Wu initially had $1062.40.

Let's break down the given information step by step:

1. Mrs. Wu spent 1/6 of her money on a dress and 2 blouses.

  Let's assume Mrs. Wu's total money is represented by the variable M. She spent 1/6 of M on the dress, which means she spent (1/6)M on the dress and the same amount on two blouses.

2. The dress cost 3 times as much as each blouse.

  Let's assume the cost of each blouse is represented by the variable B. Therefore, the cost of the dress would be 3B.

3. Mrs. Wu spent 3/4 of her remaining money on a watch.

  After spending on the dress and blouses, Mrs. Wu has (M - (1/6)M) = (5/6)M remaining. She spent 3/4 of this remaining money on a watch, which is (3/4) * (5/6)M = (15/24)M.

4. She spent $220.50 more on the watch than on the dress.

  The amount spent on the watch is (15/24)M, and the amount spent on the dress is (1/6)M. The difference between these amounts is $220.50.

To find the value of M, we can set up an equation:

(15/24)M - (1/6)M = $220.50

Simplifying the equation:

(15/24 - 1/6)M = $220.50

(5/24)M = $220.50

Multiplying both sides by (24/5):

M = $220.50 * (24/5)

M = $1062.40

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SOLUTION:

Step 1:

In this question, we are given the following:

A baseball manager is determining the batting order for the team.

The team has 9 players, but the manager definitely wants the pitcher to bat last. How many batting orders are possible.

Step 2:

The details of the solution are as follows:

Since the pitcher bats last, there is only one choice for the 9th slot.

For the 1st slot, there are 8 choices remaining.

For the 2nd slot, there are 7 choices remaining, etc.

So the number of possible batting orders is:

The maximum daily profit the company can earn is $2,350.

It is a set of points in a coordinate plane that represents the values of the function for different inputs.

The function P(x) = −6x² + 156x + 1,000 models the daily profit of the company, where x is the number of $5 price increases for each solar panel. The graph of the function has a vertex at approximately (15, 2350), which represents the maximum point on the graph.

Therefore, the maximum daily profit the company can earn is $2,350.

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Answer:

2.98

Step-by-step explanation:

First find 3% of 16.05 which is 0.48.

Then add 0.48 to 16.05 which is 16.53.

Then multiply .18 by 16.53 which gets you 2.98

Hope it helps

Answer:

To find the amount of the sales tax, we need to multiply the bill amount by the tax rate of 3% or 0.03:

Sales tax = 0.03 x $16.05 = $0.48

To find the total amount of the bill after the sales tax was added, we need to add the bill amount to the sales tax:

Total bill = $16.05 + $0.48 = $16.53

To find the amount of the tip, we need to calculate 18% of the total bill after the sales tax was added:

Tip = 0.18 x $16.53 = $2.98

Rounding to the nearest cent, Penelope left a tip of $2.98.

Step-by-step explanation:

Answer:

  x = 124

Step-by-step explanation:

You want the value of the exterior angle x°, given that the remote interior angles are 83° and 41°.

The exterior angle of a triangle is equal to the sum of the remote interior angles:

  x° = 83° +41°

  x° = 124°

  x = 124

__

Check

The interior angle adjacent to x° is its supplement:

  180° -124° = 56°

The sum of the interior angles of the triangle is 180°:

  83° +41° +56° = 180° . . . . . true

The theorem we cite above is a consequence of the fact that the missing interior angle is supplementary to both x° and the sum of the other two interior angles. It saves having to find the measure of the missing interior angle.

Answer:

98 liters

Step-by-step explanation:

add 39 and 59

Answer:

y > 3x - 1

set y = 0

0 > 3x - 1

x > 1/3

points are [ 1/3,0]

set x = 0

y > 3(0) - 1

y > - 1

points are [0,-1]

second question

x + y ≤ - 2

set x = 0

y ≤ - 2

points are [0,-2]

set y = 0

x ≤ - 2

points are [-2,0]

So therefore A should be shaded.

Answer:

47 hours?

Step-by-step explanation:

She would have 47 hours lol

If she says yes then she would have enough time to spend with family and then 1 hour to go?

Therefore, the equation of the line passing through the point (1,5) with a slope of 7 is y = 7x - 2.

The equation of a line in the point-slope form is given by the following equation:

y-y_1 = m(x-x_1)

where m is the slope of the line and (x1, y1) is any point on the line.

Therefore, we can write the equation of the line passing through the point (1,5) with a slope of 7 as follows:

y-5 = 7(x-1)

Expanding the right-hand side of the equation gives:

y-5 = 7x-7

Adding 5 to both sides of the equation gives:

y = 7x-2

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Answer:

x = 4

Step-by-step explanation:

if a line is parallel to a side of a triangle and it intersects the other two sides then id divides those sides proportionally.

DE is such a line , then

\(\frac{BD}{AD}\) = \(\frac{BE}{EC}\)  ( substitute values )

\(\frac{x+2}{x}\) = \(\frac{3}{2}\) ( cross- multiply )

3x = 2(x + 2)

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

Step-by-step explanation:

by using the paymdnt pkan, the total amount to pay is,

36 + 15×12

= £216

so saving 240-216 = 24. ( 10%)

so it is not 8% saving

The dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is 75 square meters

What is measurement?

Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, and volume, in order to describe and quantify the properties of objects and phenomena.

Let's assume that the rock wall is the width of the garden and the wire fencing is used for the length and the other two sides. Let's denote the length of the garden as L and the width as W.

Since we have 30 meters of fencing available, the total length of wire fencing used is:

L + 2W = 30 - W

Simplifying this equation, we get:

L = 30 - 3W

The area of the garden is:

A = LW

Substituting the expression for L from the previous equation, we get:

A = W(30 - 3W)

Expanding the expression, we get:

A = 30W - 3W²

To find the maximum area, we need to take the derivative of A with respect to W and set it equal to zero:

dA/dW = 30 - 6W = 0

Solving for W, we get:

W = 5

Substituting this value back into the expression for L, we get:

L = 15

Therefore, the dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is:

A = 5(15) = 75 square meters

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Answer:

\(Time = 11\frac{2}{3}\ min\)

Step-by-step explanation:

Given

\(Security\ A = 2\ mins, 20\ secs\)

\(Security\ B = 1\ mins, 40\ secs\)

Required

After how many minutes, will they round together

First, convert the given time to minutes

\(Security\ A = 2\ mins, 20\ secs\)

\(Security\ A = 2\ mins+ 20\ secs\)

\(Security\ A = 2\ mins+ \frac{20}{60}\ min\)

\(Security\ A = 2\ mins+ \frac{1}{3}\ min\)

\(Security\ A = 2\frac{1}{3}\ min\)

\(Security\ B = 1\ mins, 40\ secs\)

\(Security\ B = 1\ mins+ 40\ secs\)

\(Security\ B = 1\ mins+ \frac{40}{60}\ min\)

\(Security\ B = 1\frac{2}{3}\ min\)

So, we have:

\(Security\ A = 2\frac{1}{3}\ min\)

\(Security\ B = 1\frac{2}{3}\ min\)

List out the multiples of the time of both security personnel take round.

\(Security\ A = 2\frac{1}{3}min,\ 4\frac{2}{3}min,\ 7min,\ 9\frac{1}{3}min,\ 11\frac{2}{3}min...\)

\(Security\ B = 1\frac{2}{3}min,\ 3\frac{1}{3}min,\ 5min,\ 6\frac{2}{3}min,\ 8\frac{1}{3}min,\ 10min\ ,11\frac{2}{3}min,...\)

In the above lists, the common time is:

\(Time = 11\frac{2}{3}\ min\)

This implies that they go on round after \(11\frac{2}{3}\ min\)

Answer:

Step-by-step explanation:

what is 12/21 + 18/21 + 14/21

(12 + 18 + 14)/21 =

44/21

The distance between points R and S is  \(\sqrt{ (185)\). The correct answer is D. She made no errors.

Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is shown:

RS = √(-4) (-3))² + (7 − 5)²

= √(-1)² + (2)²= √1 + 4

= √5

The error is with the order of subtraction in the formula for the distance between two points.

Heather did not make any errors in calculating the distance between two points. Therefore, the correct answer to the question above is (OD) She made no errors.

The formula for the distance between two points, A (x1, y1) and B (x2, y2), in the coordinate plane is given as;

dAB = \(\sqrt{  ((x^2 - x1)^2 + (y2 - y1)^2)\)

Comparing the given question with the formula above, we have;

A = R (-3, -4) and B = S (5, 7)The distance, AB = RS.

Therefore, we have;

RS = \(\sqrt{ ((5 - (-3))^2 + (7 - (-4))^2)\)

On solving the above equation;RS = \(\sqrt{ ((5 + 3)^2 + (7 + 4)^2)\)RS

= \(\sqrt{ (8^2 + 11^2)RS\)

= \(\sqrt{ (64 + 121)RS\)

= \(\sqrt{ (185)\)

Therefore, the distance between points R and S is  \(\sqrt{ (185)\).

From the calculation, it is clear that Heather did not make any errors while calculating the distance between two points. The answer obtained by Heather is correct.

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Answer:

$26,986.29

Step-by-step explanation:

We can use the formula for calculating the depreciation of an asset over time:

wor

\(\bold{D = P(1 - \frac{r}{100} )^t}\)

where:

D= the current value of the asset

P = the initial purchase price of the asset

r = the annual depreciation rate as a decimal

t = the number of years the asset has been in use

In this case, we have:

P = $39,600

r = 12% = 0.12

t = 3 years

Substituting these values into the formula, we get:

\(D= 39,600(1 - \frac{12}{100})^3\\D= 39,600(1 - 0.12)^3\\D= 39,600*0.88^3\\D= 39,600*0.681472\\D=26986.2912\)

Therefore, the car is worth approximately $26,986.29 after 3 years of depreciation at a rate of 12% per annum.

Answer:

$26,986.29

Step-by-step explanation:

As the car's value depreciates at a constant rate of 12% per annum, we can use the exponential decay formula to create a function for the value of the car f(t) after t years.

\(\boxed{f(t)=a(1-r)^t}\)

where:

In this case, the initial value is $39,600, and the rate of depreciation is 12% per year. Therefore, the function that models the value of the car after t years is:

\(f(t)=39600(1-0.12)^t\)

\(f(t)=39600(0.88)^t\)

To calculate the value of the car after 3 years, substitute t = 3 into the function:

\(\begin{aligned} f(3)&=39600(0.88)^3\\&=39600(0.681472)\\&=26986.2912\\&=26986.29\;(\sf 2\;d.p.)\end{aligned}\)

Therefore, the car is worth $26,986.29 after 3 years.

The table with correct values of A, B and C is,

⇒ Donuts   2        4        5        8

    Cost     13.80 27.60 34.50 55.20

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

We have to given that;

The table below shows the ratios of boxed donuts to the cost.

Donuts    A       4        5     C

Cost    13.80  27.60   B   55.20

Now, By definition of ratio, we get;

⇒ A / 13.80 = 4 / 27.60

⇒ A = 13.80 × 4 / 27.60

⇒ A = 2.00

And,

⇒ 4 / 27.60 = 5 / B

⇒ B = 5 × 27.60 / 4

⇒ B = 34.5

⇒ 4 / 27.60 = C / 55.20

⇒ C = 55.20 × 4 / 27.60

⇒ C = 8

Thus, The table with correct values of A, B and C is,

⇒ Donuts   2        4        5        8

    Cost     13.80 27.60 34.50 55.20

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Answer:

a

Step-by-step explanation:

i took the test :)

Answer: well solve what's in the parentheses first

Step-by-step explanation: that is the first step